Systems and methods for downlink scheduling in multiple input multiple output wireless communications systems

ABSTRACT

Systems and methods for downlink scheduling in wireless communications systems are described. In some embodiments, a method includes: applying channel prediction at a transmitter for transmitting information to one or more mobile devices; predicting channel state information for a channel over which the information is transmitted, the channel state information being based, at least, on the channel prediction; determining a precoding matrix to apply to the information, the determining the precoding matrix being based, at least, on predicted channel state information; and scheduling transmission of the information to the one or more mobile devices based, at least, on an asymptotic ergodic rate for the one or more mobile devices. The asymptotic ergodic rate can be based on large-scale channel behavior and a maximum Doppler shift between the mobile devices.

CROSS REFERENCE TO RELATED APPLICATION AND CLAIM OF PRIORITY

This application is a non-provisional of, and claims the benefit of,U.S. Provisional Patent Application No. 61/551,285, filed Oct. 25, 2011,and titled “Downlink Scheduling in Network MIMO Using Two-Stage ChannelState Feedback,” which is incorporated herein by reference in itsentirety.

TECHNICAL FIELD

The disclosed matter generally relates to wireless communications, and,more particularly, to downlink scheduling for wireless communications.

BACKGROUND

A multiple input multiple output (MIMO) architecture of a system can beemployed to improve the throughput of broadband wireless networks. Inconventional cellular networks, frequency reuse among nearby cells canresult in inter-cell interference (ICI) and degrade the performance. Toovercome these problems, base station (BS) cooperation can be employed.For exemple, assuming perfect backhaul connection, a network of multiplecells can be viewed as a virtual MIMO system, and the mobiledevices/users in the multiple cells can be jointly served by multipleBSs.

In a resource unit, the cooperating BSs in one cluster can jointlyselect a set of active mobile devices/users. Precoding can be appliedfor the selected mobile devices/users. The precoding can be applied suchthat the signal intended for each of the selected mobile devices/usersis received with lower interference than the interference for thesignals for which precoded is not applied. The precoding can be linearprecoding, such as for MU-MIMO based on block diagonalization (BD), inwhich the signal for each user is projected onto the nullspace of theaugmented channel matrix of other mobile devices/users. Precoding can beperformed for clustered MIMO networks with inter-cluster coordination.Additionally, greedy user selection algorithms can be employed forsingle-cell multi-user MIMO (MU-MIMO) networks based on BD precoding.However, the above described precoding techniques assume perfect channelstate information at the transmitter (CSIT). To achieve, or at leastapproximate, CSIT, feedback from the mobile devices/users is employed.Unfortunately, the overhead introduced by CSIT feedback limits theperformance of MIMO systems. For multi-cell networks with large numberof mobile devices/users, further feedback reduction is desired. Otherproblems with the state of the art and corresponding benefits of some ofthe various non-limiting embodiments may become further apparent uponreview of the following detailed description.

SUMMARY

The following presents a simplified summary of the disclosed subjectmatter in order to provide a basic understanding of some embodiments ofthe disclosed subject matter. This summary is not an extensive overviewof the disclosed subject matter. It is intended to neither identify keyor critical elements of the disclosed subject matter nor delineate thescope of the disclosed subject matter. Its sole purpose is to presentsome concepts of the disclosed subject matter in a simplified form as aprelude to the more detailed description that is presented later.

In some embodiments, a method includes: applying channel prediction at atransmitter in connection with transmitting information to one or moremobile devices; predicting channel state information for a channel overwhich the information is transmitted, the channel state informationbeing based, at least, on the channel prediction; determining aprecoding matrix to apply to the information based, at least, onpredicted channel state information from the predicting; and schedulingtransmission of the information to the one or more mobile devices based,at least, on an asymptotic ergodic rate for the one or more mobiledevices

In some embodiments, a device includes: a channel prediction componentconfigured to apply channel prediction at a transmitter for transmittinginformation to one or more mobile devices; and a channel stateinformation prediction component configured to predict channel stateinformation for a channel over which the information is transmitted, thechannel state information being based, at least, on the channelprediction. The device can also include: a precoding matrix componentconfigured to determine a precoding matrix to apply to the information,wherein determination of the precoding matrix is based, at least, onpredicted channel state information; and a scheduling componentconfigured to schedule transmission of the information to the one ormore mobile devices based, at least, on an asymptotic ergodic rate forthe one or more mobile devices.

In some embodiments, another method includes: obtaining statisticalinformation of a channel over which the one or more mobile devicestransmit; determining an ergodic rate based, at least, on thestatistical information; selecting one or more mobile devices forscheduling based, at least, on the ergodic rate; and scheduling the oneor more mobile devices based, at least, on variation in the channel.

In some embodiments, another method includes: receiving, at a firstlocation in a frame, frame-level feedback from the one or more mobiledevices; determining an asymptotic ergodic rate based, at least, on theframe-level feedback; and selecting at least one of the one or moremobile devices to receive downlink transmission of information duringthe frame.

In some embodiments, another method includes: selecting at least one ofa single user mode or a multi-user mode, the selecting comprisingselecting a mode associated with a higher one of a first weightedasymptotic ergodic rate or a second weighted asymptotic ergodic rate;and scheduling one or more mobile devices to receive information in aselected one of the single user mode or the multi-user mode.

In some embodiments, a computer-readable storage medium is described.The computer-readable storage medium can have computer-executableinstructions that, in response to execution, cause a computing deviceincluding a processor to perform operations, comprising: applyingchannel prediction at a transmitter in connection with transmission ofinformation to one or more mobile devices; predicting channel stateinformation for a channel over which the information is transmittedbased, at least, on the channel prediction; determining a precodingmatrix to apply to the information based, at least, on predicted channelstate information; and scheduling transmission of the information to theone or more mobile devices based, at least, on an asymptotic ergodicrate for the one or more mobile devices.

To the accomplishment of the foregoing and related ends, the disclosedsubject matter, then, comprises the features hereinafter fullydescribed. The following description and the annexed drawings set forthin detail certain illustrative embodiments of the disclosed subjectmatter. However, these embodiments are indicative of but a few of thevarious ways in which the principles of the disclosed subject matter maybe employed. Other embodiments, advantages and novel features of thedisclosed subject matter will become apparent from the followingdetailed description of the disclosed subject matter when considered inconjunction with the drawings.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a diagram of an exemplary system that can facilitate downlinkscheduling in wireless communications systems in accordance with variousembodiments of the disclosed subject matter.

FIG. 2 is an illustration of a block diagram of an exemplary centralcontrol unit that can facilitate downlink scheduling in wirelesscommunications systems in accordance with various embodiments of thedisclosed subject matter.

FIG. 3 is an illustration of a block diagram of an exemplary mobileterminal for which downlink scheduling can be facilitated in accordancewith various embodiments of the disclosed subject matter.

FIG. 4 is an illustration of a block diagram of an exemplary basestation that can transmit information according to downlink schedulingmethods in accordance with various embodiments of the disclosed subjectmatter.

FIGS. 5, 6, 7, 8A and 8B are flowcharts of exemplary methods tofacilitate downlink scheduling in wireless communications systems inaccordance with various embodiments of the disclosed subject matter.

FIG. 9 is an exemplary graph of sum rate versus cell edgesignal-to-noise ratio (SNR) with comparison of simulation andapproximation for a selected number of antennas in accordance withvarious embodiments of the disclosed subject matter.

FIG. 10 is an exemplary graph of sum capacity versus number of mobiledevices/users employing downlink scheduling in accordance with variousembodiments of the disclosed subject matter.

FIG. 11 is an exemplary graph of an Average Jain's Fairness Index versusobservation window size employing downlink scheduling in accordance withvarious embodiments of the disclosed subject matter.

FIG. 12 is an exemplary schematic block diagram illustrating a suitableoperating environment to facilitate the downlink scheduling describedherein.

FIG. 13 is a block diagram of an exemplary electronic device that canfacilitate downlink scheduling for wireless network components inaccordance with various embodiments of the disclosed subject matter.

DETAILED DESCRIPTION

The disclosed subject matter is now described with reference to thedrawings, wherein like reference numerals are used to refer to likeelements throughout. In the following description, for purposes ofexplanation, numerous specific details are set forth in order to providea thorough understanding of the disclosed subject matter. It may beevident, however, that the disclosed subject matter may be practicedwithout these specific details. In other instances, well-knownstructures and devices are shown in block diagram form in order tofacilitate describing the disclosed subject matter.

As used in this application, the terms “component,” “system,”“platform,” and the like can refer to a computer-related entity or anentity related to an operational machine with one or more specificfunctionalities. The entities disclosed herein can be either hardware, acombination of hardware and software, software, or software inexecution. For example, a component may be, but is not limited to being,a process running on a processor, a processor, an object, an executable,a thread of execution, a program, and/or a computer. By way ofillustration, both an application running on a server and the server canbe a component. One or more components may reside within a processand/or thread of execution and a component may be localized on onecomputer and/or distributed between two or more computers. Also, thesecomponents can execute from various computer readable media havingvarious data structures stored thereon. The components may communicatevia local and/or remote processes such as in accordance with a signalhaving one or more data packets (e.g., data from one componentinteracting with another component in a local system, distributedsystem, and/or across a network such as the Internet with other systemsvia the signal).

In addition, the term “or” is intended to mean an inclusive “or” ratherthan an exclusive “or.” That is, unless specified otherwise, or clearfrom context, “X employs A or B” is intended to mean any of the naturalinclusive permutations. That is, if X employs A; X employs B; or Xemploys both A and B, then “X employs A or B” is satisfied under any ofthe foregoing instances. Moreover, articles “a” and “an” as used in thespecification and annexed drawings should generally be construed to mean“one or more” unless specified otherwise or clear from context to bedirected to a singular form.

Moreover, terms like “user equipment,” “mobile station,” “mobile,”“subscriber station,” “communication device,” “access terminal,”“terminal,” “handset,” and similar terminology, refer to a wirelessdevice (e.g., cellular phone, smart phone, computer, personal digitalassistant (PDA), set-top box, Internet Protocol Television (IPTV),electronic gaming device, multi-media recorder/player, videorecorder/player, audio recorder/player, printer, etc.) utilized by asubscriber or user of a wireless communication service to receive orconvey data, control, voice, video, sound, gaming, or substantially anydata-stream or signaling-stream. The foregoing terms are utilizedinterchangeably in the specification and related drawings. Likewise, theterms “access point,” “base station,” “Node B,” “evolved Node B,” “homeNode B (HNB),” and the like, are utilized interchangeably in theapplication, and refer to a wireless network component or appliance thatserves and receives data, control, voice, video, sound, gaming, orsubstantially any data-stream or signaling-stream from a set ofsubscriber stations. Data and signaling streams can be packetized orframe-based flows.

Systems and methods disclosed herein relate to downlink scheduling inwireless communications systems. In particular, the downlink schedulingcan employ a two-stage feedback mechanism in which channel stateinformation is predicted and employed. A central control unit cancommunicate the downlink scheduling information to one or more basestations (BSs) that transmit information to selected mobile devices. Thedownlink scheduling can be based on an asymptotic ergodic rate for themobile devices. The asymptotic ergodic rate, which can be a function oflarge-scale channel behavior and the maximum Doppler shift of the mobiledevices.

To perform the downlink scheduling, the central control unit can applychannel prediction at a BS for transmitting information to one or moremobile devices, and predict channel state information for a channel overwhich the information is to be transmitted. The channel stateinformation can be based on the channel prediction. The central controlunit can also determine a precoding matrix to apply to the informationprior to transmission by the BS. The precoding matrix can be based onthe predicted channel state information.

In various embodiments, the systems and methods can advantageouslyprovide the asymptotic ergodic rate as a function of large-scale fadingand Doppler shift of the one or more mobile devices. The systems andmethods can achieve higher mobile device spectral efficiency andfairness with lower feedback overhead to the central control unit fromthe mobile devices.

Turning now to the drawings, FIG. 1 is a diagram of an exemplary systemthat can facilitate downlink scheduling in wireless communicationssystems in accordance with various embodiments of the disclosed subjectmatter. The system 100 can be a MIMO system. The system 100 can includeone or more BSs 102, 104 and a central control unit 110. In variousembodiments, the system 100 can also include one or more mobile devices106, 108. The BSs 102, 104, mobile devices 106, 108 and/or centralcontrol unit 110 can be electrically and/or communicatively coupled toone or another to perform one or more functions of the system 100.

The one or more mobile devices 106, 108 can include one or moreantennae. In various embodiments, the mobile devices 106, 108 can beconfigured to transmit feedback to the one or more BSs 102, 104 and/orthe central control unit 110 for facilitating downlink schedulingmethods described herein.

In some embodiments, one or more of the mobile devices can includestructure such as that shown in FIG. 3. FIG. 3 is an illustration of ablock diagram of an exemplary mobile terminal for which downlinkscheduling can be facilitated in accordance with various embodiments ofthe disclosed subject matter.

As shown, a mobile device 300 can include a communication component 302configured to transmit and/or receive information between the BSs and/orthe central control unit 200. For example, the communication component302 can transmit feedback information to the central control unit 200and/or receive information transmitted on the downlink channel from oneor more of the BSs.

The feedback component 304 can be configured to generate the feedbacktransmitted to the central control unit 200.

The scheduling component 306 can be configured to receive schedulinginformation including, but not limited, information indicative of a timethat the mobile device can expect to receive transmitted informationfrom the one or more BSs.

The mobile device 300 can also include a memory 308 configured to storeinformation and/or computer-executable instructions.

The mobile device 300 can also include a microprocessor 310 configuredto execute the computer-executable instructions to perform one or morefunctions of the mobile device 300.

The BSs 102, 104 can be configured to transmit and receive informationto and from mobile devices 106, 108. In various embodiments, the BSs102, 104 can be multi-antenna BSs for facilitating the MIMOarchitecture. The transmission of information can be according to adownlink schedule determined by the central control unit 110 in someembodiments.

In some embodiments, one or more of the BSs can include structure suchas that shown in FIG. 4. FIG. 4 is an illustration of a block diagram ofan exemplary base station that can transmit information according todownlink scheduling methods in accordance with various embodiments ofthe disclosed subject matter.

The BS 400 can include a communication component 402 configured totransmit and/or receive information between the mobile devices and/orthe central control unit 200. For example, the communication component402 can receive scheduling information from the central control unit 200and/or transmit information to the mobile devices on the downlinkchannel.

The scheduling component 404 can be configured to receive schedulinginformation including, but not limited, information indicative of atime, frame and/or slot during which the BS should transmit informationto the mobile devices. The scheduling information can also includeinformation identifying one or more mobile devices to which the BSshould transmit information.

The BS 400 can also include a memory 406 configured to store informationand/or computer-executable instructions.

The BS 400 can also include a microprocessor 408 configured to executethe computer-executable instructions to perform one or more functions ofthe BS 400.

The central control unit 110 can be configured to determine a schedulefor downlink transmission from one or more of the BSs 102, 104 to one ormore of the mobile devices 106, 108 as described herein and withreference to FIG. 2.

Microprocessor 112 can perform one or more of the functions described inthis disclosure with reference to any of the systems and/or methodsdisclosed. The memory 114 can be a computer-readable storage mediumstoring computer-executable instructions and/or information forperforming the functions described in this disclosure with reference toany of the systems and/or methods disclosed. For example, as shown,memory 114 can store computer-executable instructions that can beexecuted by a computing device to cause the computing device to performoperations of the systems and/or methods described herein. In variousembodiments, the computing device can include, but is not limited to,one or more of the BSs 102, 104, the central control unit 110 and/or oneor more of the mobile devices 106, 108. While FIG. 1 shows themicroprocessor 112 and memory 114 at central control unit 110, one ormore of the microprocessor 112 and/or memory 114 can be communicativelycoupled to or within one or more of the BSs 102, 104 and/or the mobiledevices 106, 108.

FIG. 2 is an illustration of a block diagram of an exemplary centralcontrol unit that can facilitate downlink scheduling in wirelesscommunications systems in accordance with various embodiments of thedisclosed subject matter. The central control unit 200 can be or caninclude one or more of the structure and/or functionality of the centralcontrol unit 110 of FIG. 1 in some embodiments. The central control unit200 can include a communication component 202, a channel predictioncomponent 204, a channel state information prediction component 206, aprecoding matrix component 208, an asymptotic ergodic rate calculationcomponent 210, a scheduling component 212, a microprocessor 214 and/or amemory 216. The communication component 202, channel predictioncomponent 204, channel state information prediction component 206,precoding matrix component 208, asymptotic ergodic rate calculationcomponent 210, scheduling component 212, microprocessor 214 and/ormemory 216 can be communicatively or electrically coupled to one anotherto perform one or more functions of the central control unit 200.

In some embodiments, the communication component 202 can be configuredto transmit and/or receive information to and from the one or moremobile devices or the one or more BSs in the MIMO network to which thecentral control unit 200 is communicatively coupled. For example, thecommunication component 202 can receive feedback information from theone or more mobile devices and/or transmit a downlink schedule forcommunication between the one or more BSs and one or more of the mobiledevices.

The channel prediction component 204 can be configured to apply channelprediction at a transmitter for transmitting information to one or moremobile devices.

The channel state information prediction component 206 can be configuredto predict channel state information for a channel over which theinformation is transmitted, the channel state information being based,at least, on the channel prediction.

The precoding matrix component 208 can be configured to determine aprecoding matrix to apply to the information. In some embodiments,determination of the precoding matrix is based, at least, on predictedchannel state information.

The scheduling component 212 can be configured to schedule transmissionof the information to the one or more mobile devices on the downlinkchannel. The downlink schedule can be based, at least, on an asymptoticergodic rate for the one or more mobile devices.

The functionality of the central control unit 200 can be as follows invarious embodiments. The following notations are used in thisdisclosure. Normal letters represent scalar quantities; and uppercaseand lower case boldface letters denote matrices and vectors,respectively. Additionally, the square over the upper left corner of aletter represents a circumflex (^) over the letter. Also, ( )^(T) and ()^(H) stand for the transpose and conjugate transpose, respectively.[T]_((r,e)) denotes the sub-matrix of T generated by selecting the rowsand columns indexed by vectors r and c respectively, and the symbol “:”is used to represent all columns or all rows. E[.] is the expectation ofthe variable or expression inside the bracket. I_(N) represents theidentity matrix with size N.

In some embodiments, the system model and channel prediction can beperformed as described below. In some embodiments, the channelprediction component 204 can perform the channel prediction and systemmodeling.

The received channel model can be as follows. The aggregated channelcoefficient matrix of user u from all the B cooperating BSs can berepresented as shown in Equation (1)H _(u)=[ρ_(u,1) H _(u,1), . . . , ρ_(u,B) H _(u,B)]  (1)where H_(u,b) εC^(N) ^(e) ^(×N) ^(t) can represent the small-scalefading channel matrix associated with user u and BS b, and where N_(t)and N_(r) can be the number of antennas of one BS and one user,respectively. The variable, ρ_(u,b), can represent the large-scalefading behavior, including pathloss and shadowing. The coefficients inH_(u,b) can be modeled as wide-sense stationary (WSS), narrow-bandcomplex Gaussian processes. The received signal of user u can be writtenas

$\begin{matrix}{y_{u} = {{H_{u}T_{u}x_{u}} + {H_{u}{\sum\limits_{u^{\prime} \neq u}^{\;}{T_{u^{\prime}}x_{u^{\prime}}}}} + n_{u}}} & (2)\end{matrix}$where T_(u)=[T_(u,1), . . . , T_(u,B)] can be the aggregated precodermatrix with orthonormal columns, x_(u) can be the transmitted signal andn_(u) can be a white complex Gaussian noise vector with covariancematrix σ²I_(N) _(r) . The second term in (2) can represent themulti-user interference (MUI). In some embodiments, BD precoding can beperformed by a precoding matrix component 208. With BD precoding andperfect CSIT, in some embodiments, the MUI can be eliminated bytransmitting the signal of one user on the nullspace of the augmentedchannel matrix of other simultaneously, or concurrently, selected mobiledevices/users.

In the embodiments described herein, channel prediction can be appliedto generate a hypothesized channel coefficient matrix, which can beemployed to determine the precoding matrix before transmitting one ormore of the symbols. In some embodiments, channel prediction can beapplied to generate a hypothesized channel coefficient matrix, which canbe employed to determine the precoding matrix before transmitting eachof the symbols. In some embodiments, the MUI is not perfectly cancelleddue to the channel prediction inaccuracy, which is discussed below.

In some embodiments, an auto-regressive model for channel prediction canbe as follows. In some embodiments, the CSIT can be predicted by thechannel state prediction component 206. The CSIT can be employed forprecoding before transmission. The autoregressive (AR) model can bebased on previous channel feedback to predict the channel coefficientsof one or more future slots. For example, in some embodiments, a MIMOchannel with Rayleigh fading can be modeled. The variable, h^(r,t) (n),can be the small-scale channel coefficient of link (r,t) in slot n, andthe Jake's model by which the autocorrelation function (ACF) of channelcoefficients is described as a function of symbol difference m can be asfollows in Equation (3):φ_(u) ^(r,s)(m)=E[h ^(r,t)(n)h ^(r,t) ^(H) (n+m)]=J ₀(2πf _(d) T _(slot)m)  (3)where J₀(·) can represent the Bessel function of the first kind of order0, T_(slot) can be the slot duration and f_(d) can be the maximumDoppler frequency shift. The dynamic system of channel variation can bemodeled as an AR process with order p as shown in Equation (4):

$\begin{matrix}{{h_{u}^{r,t}(n)} = {{\sum\limits_{i = 1}^{p}{a_{i,u}{h_{u}^{r,t}\left( {n - i} \right)}}} + {v_{u}^{r,t}(n)}}} & (4)\end{matrix}$where α_(i,u) are the coefficients of the AR process. In someembodiments, these coefficients can be determined by solving theYule-Walker equations, and the prediction error v_(u) ^(r,t) (n) can bezero-mean Gaussian distributed with variance ε_(u) ² represented byEquation (5):

$\begin{matrix}{ɛ_{u}^{2} = {{\phi_{u}^{r,t}(0)} + {\sum\limits_{i = 1}^{p}{a_{i,u}{\phi_{u}^{r,t}(i)}}}}} & (5)\end{matrix}$

Applying the channel prediction model, the actual channel matrix H_(u)can be represented as shown in Equation (6):H _(u) =H _(u) ^((P)) +E _(u)  (6)where H_(u) ^((P)) and E_(u) can be the predicted channel and channelprediction error matrices, respectively. Similar to Equation (1), thesetwo matrices can be expressed as shown in Equations (7) and (8):H _(u) ^((P))=[ρ_(u,1) H _(u,1) ^((P)) . . . ρ_(u,B) H _(u,B)^((P))]  (7)E _(u)=[ρ_(u,1) E _(u,1) . . . ρ_(u,B) E _(u,B)]  (8)

The elements in H_(u) ^((P)) and E_(u) can represent zero mean Gaussianrandom variables with variance 1−ε_(u) ² and ε_(u) ², respectively.Higher maximum Doppler shift can correspond to higher ε_(u) ². Also, inthis embodiment, perfect channel estimation at the receiver and perfectfeedback can be assumed. If channel estimation or feedback error is tobe considered, a Kalman filter can be applied.

In some embodiments, the asymptotic ergodic rate calculation component210 can perform asymptotic ergodic rate analysis as follows.Specifically, an asymptotic ergodic capacity analysis for network MIMOsystems for single-user (SU) and multi-user (MU) cases can be asdescribed. In some embodiments, total power constraint (TPC) in one ormore clusters can be applied instead of per BS power constraint (PBPC)for better tractability. In some embodiments, total power constraint(TPC) in each cluster can be applied instead of per BS power constraint(PBPC) for better tractability. With TPC and equal power allocation foreach stream, the transmission power for one stream can be given byγ=P/(N,M) for all user u, where cluster power constraint P, and N_(r)streams can be assumed to be assigned to each of the totally M selectedmobile devices/users. In some embodiments, the asymptotic rates can berepresented as functions of the large-scale fading behavior of thechannel and the Doppler shift.

In some embodiments, a model for an approximately equivalent channelmatrix can be as follows. For single-cell MIMO systems with independentidentically distributed (i.i.d.) Gaussian channel coefficients,asymptotic rate can be analyzed. To find the asymptotic ergodic rate fornetwork MIMO systems where the elements of the aggregated channel matrixare not always i.i.d. Gaussian random variables, the network MIMOchannel matrix can be transformed into a virtual single cell MIMOchannel.

The following definition can be employed. Definition 1: Let z_(i)εC^(q×1), i=1, . . . l be multivariate normal distributed vectors withzero mean and covariance matrix C, and Z denotes the q×l matrix composedof the column vectors z_(i), then the matrix ZZ^(H) has a centralWishart distribution with covariance matrix C and l degrees of freedom,denoted as ZZ^(H):CW_(i)(0, C). H_(u)H_(u) ^(H)=Σ_(b=1) ^(B)ρ_(u,b)²H_(u,b)H_(u,b) ^(H) can be a linear combination of central Wishartmatrices, and the row vectors can have identical covariance matrix.

The distribution can be approximated as shown in Equations (9), (10) and(11):

$\begin{matrix}{{H_{u}{H_{u}^{H}:{{CW}_{N_{t,u}}\left( {0,{\rho_{u}I_{N_{r}}}} \right)}}}{where}} & (9) \\{{N_{t,u} = {N_{t}\left\lbrack \frac{\left( {\sum\limits_{b}^{B}\rho_{u,b}} \right)^{2}}{\sum\limits_{b}^{B}\rho_{u,b}^{2}} \right\rbrack}}{and}} & (10) \\{\rho_{u} = \left( \frac{\sum\limits_{b}^{B}\rho_{u,b}^{2}}{\sum\limits_{b}^{B}\rho_{u,b}} \right)} & (11)\end{matrix}$

The above approximation can be interpreted as if the mobile device iscommunicating with a virtual BS with N_(t,u) transmitting antennas, andthe channel can be modeled as an equivalent N_(r)×N_(t,u) channel matrixρ_(u) H_(u), where H_(u) can be the equivalent small-scale fading matrixand ρ_(u) can be the equivalent large-scale fading parameter. Sinceρ_(u) can be determined by the large-scale fading gain from differentBSs, ρ_(u) can be viewed that the mobile device is actually served bythe antennas from BSs with larger ρ_(u,b)'s.

In some embodiments, the asymptotic rate for SU-MIMO can be as follows.In some embodiments, methods can be employed for instances wherein onlya single mobile device is served in the multi-cell network. Theorem 1can be utilized for these embodiments. Theorem 1: Under single mobiledevice network MIMO transmission, as BN_(t),N_(r)→∝ with BN_(t)/Nr=β,the asymptotic ergodic rate with normalized thermal noise power can beapproximated by Equation (12):

$\begin{matrix}{{\frac{C_{su}\left( {\beta,\gamma} \right)}{N_{r}} = {{\log\left\lbrack {1 + {\beta\hat{\gamma}} - {F\left( {\beta,\hat{\gamma}} \right)}} \right\rbrack} + {\beta\;{\log_{2}\left\lbrack {1 + {\beta\hat{\gamma}} - {F\left( {\beta,\hat{\gamma}} \right)}} \right\rbrack}} - {{\log_{2}(e)}{F\left( {\beta,\hat{\gamma}} \right)}}}}\mspace{79mu}{where}\mspace{79mu}{{F\left( {x,y} \right)} = {\frac{1}{4}\left\lbrack {\sqrt{1 + {y\left( {1 + \sqrt{x}} \right)}^{2}} - \sqrt{1 + {y\left( {1 - \sqrt{x}} \right)}^{2}}} \right\rbrack}}\mspace{79mu}{{\beta = {{\left( {N_{t,u}/N_{t,u}} \right)\beta} = {N_{t,u}/N_{r}}}},{\hat{\gamma} = {\rho_{u}^{2}{\gamma.}}}}} & (12)\end{matrix}$

The proof can be as follows. Proof Construct an equivalent small-scalechannel matrix H_(u) with size N_(r)×N_(t) and i.i.d. zero mean Gaussianelements with unit variance. The ergodic rate without CSIT can bewritten as shown in Equation (13):

$\begin{matrix}{C_{noCSIT} = {E\left\lbrack {\log_{2}{\det\left( {I_{N_{r}} + {\frac{\hat{\gamma}}{N_{t,u}}H_{u}H_{u}^{H}}} \right)}} \right\rbrack}} & (13)\end{matrix}$

Then an asymptotic ergodic capacity formula for SU-MIMO can be adoptedto obtain Equation (14):

$\begin{matrix}{\frac{C_{noCSIT}\left( {\beta,\hat{\gamma}} \right)}{N_{r}} = {{\log\left\lbrack {1 + \hat{\gamma} - {F\left( {\beta,{\hat{\gamma}/\beta}} \right)}} \right\rbrack} + {\beta\;{\log_{2}\left\lbrack {1 + {\hat{\gamma}/\beta} - {F\left( {\beta,{\hat{\gamma}/\beta}} \right)}} \right\rbrack}} - {\beta\frac{\log_{2}(e)}{\hat{\gamma}}{F\left( {\beta,{\hat{\gamma}/\beta}} \right)}}}} & (14)\end{matrix}$

For N_(t,u)>N_(r), the transmission power can be concentrated on theN_(r) non-zero eigenmodes to improve the capacity. With predicted CSIT,optimal water-filling power allocation cannot be found in someembodiments. Hence a simpler way to equally allocate the power to thenon-zero eigenmodes can be identified, thenC_(su)=C_(noCSIT)(β,β{circumflex over (γ)}) can result.

In some embodiments, an asymptotic rate for multi-user MIMO can be asfollows. In some embodiments, the BD precoder for mobile device/user ucan be designed, based on the predicted CSIT, as T_(u) ^((P)). The BDprecoder can be implemented by the precoding matrix component 208 insome embodiments. The CSIT can be predicted by the channel stateinformation prediction component 206 in some embodiments.

The received signal can be rewritten as shown in Equation (15):

$\begin{matrix}{y_{u} = {{H_{u}T_{u}^{(P)}x_{u}} + {E_{u}{\sum\limits_{u^{\prime} \neq u}{T_{u^{\prime}}^{(P)}x_{u^{\prime}}}}} + n_{u}}} & (15)\end{matrix}$The achievable rate of mobile device/user u can be represented byEquation (16) as follows.R _(u) ^((P)) =E{log₂det(I+γ _(u) H _(u) T _(u) ^((P)) T _(u) ^((P))^(H) H _(u) ^(H) R _(u) ⁻¹)}  (16)where R_(u) ⁻¹ is the interference plus noise covariance matrix given byEquation (17)

$\begin{matrix}{R_{u} = {{{E_{u}\left( {\sum\limits_{u^{\prime} \neq u}{\gamma_{u^{\prime}}T_{u^{\prime}}^{(P)}T_{u^{\prime}}^{{(P)}^{H}}}} \right)}E_{u}^{H}} + {\sigma^{2}{I_{N_{r}}.}}}} & (17)\end{matrix}$Before deriving the asymptotic rate for MU-MIMO case, the followinglemma can be employed.

Lemma 1: Consider N complex random variables x_(i), i=1, N with Σ_(t=1)^(N)∥x_(i)∥²=1. If ∥x_(i)∥²'s are independent uniformly distributed, asN→∝, the distribution of summation of K randomly selected ∥x_(k)∥²concentrates toward K/N.

Theorem 2: For a network MIMO system with imperfect CSIT, the asymptoticresults for the achievable rate in MU mode can be approximated as shownin Equation (18)

$\begin{matrix}{\frac{R_{u}}{N_{r}} \approx {{\sum\limits_{u^{\prime} \neq u}{\log_{2}\left( \frac{1 + {N_{r}\rho_{u}^{2}\gamma_{u^{\prime}}{\kappa ɛ}_{u}^{2}\eta_{1}}}{1 + {N_{r}\rho_{u}^{2}\gamma_{u^{\prime}}{\kappa ɛ}_{u}^{2}\eta_{2}}} \right)}} + {\log_{2}\left( {1 + {N_{r}\gamma_{u}\rho_{u}^{2}{\kappa\eta}_{1}}} \right)} + {\log_{2}\frac{\eta_{2}}{\eta_{1}}} + {\left( {\eta_{2} - \eta_{1}} \right)\log_{2}e}}} & (18)\end{matrix}$where γ_(u) can be the transmission power for data streams of mobiledevice/user u under normalized thermal noise. The variables κ, η₁ and η₂are given in the proof. Proof. Using the Wishart matrix approximation,the received signal for mobile device/user u can be re-written as shownin Equation (19)

$\begin{matrix}{y_{u} = {{H_{u}T_{u}x_{u}} + {E_{u}{\sum\limits_{u^{\prime} \neq u}{T_{u^{\prime}}^{(P)}x_{u^{\prime}}}}} + n_{u}}} & (19)\end{matrix}$where H_(u) can be the equivalent channel matrix with size ofN_(r)×N_(t,u), and T_(u) can be the N_(t,u)×N_(r) equivalent precodingmatrix to match H_(u). Let g=[g₁, . . . , g_(N) _(t,u) ] be the columnindex of consisting of biggest large-scale fading coefficients. Theequivalent precoding matrix can be given by selecting the correspondingrows from the N_(r)×BN_(t) precoding matrix T_(u) ^((P)), that is,T_(u)=[T_(u) ^((P))]_((g,;)). With approximation method similar to thatapplied to channel matrix, the equivalent CSIT error matrix E_(u)εC^(N)^(r) ^(×N) ^(t,u) can have zero mean Gaussian distributed elements withvariance ε_(u) ². Treating the MUI as noise, the achievable rate ofmobile device/user u can be re-written as shown in Equation (20)R _(u) =E[log₂ det(R _(u)+γ_(u)ρ_(u) ² H _(eff,u) H _(eff,u)^(H))]−E[log₂ det(R _(u))]  (20)where H_(eff,u)=H_(u)T_(u) can be the effective small-scale channelmatrix for mobile device/user u, and R_(u) can be the equivalentinterference-plus-noise covariance matrix shown in Equation (21):

$\begin{matrix}{R_{u} = {I_{N_{r}} + {{E_{u}\left\lbrack {\sum\limits_{u^{\prime} \neq u}{\gamma_{u^{\prime}}\rho_{u}^{2}T_{u^{\prime}}T_{u^{\prime}}^{H}}} \right\rbrack}E_{u}^{H}}}} & (21)\end{matrix}$

Since T_(u) is independent of H_(u), the elements in H_(eff,u) arelinear combinations of i.i.d. standard Gaussian random variables, whichare zero mean Gaussian distributed with variance equal to the summationof the square of the coefficients in linear combination. Let t_(i) bethe ith column of T_(u) ^((P)), in some embodiments, if there is noknowledge of the small-scale fading behavior, the elements of t_(i) canbe assumed to be independent uniformly distributed. The correspondingrows from T_(u) ^((P)) can be selected to form the equivalent precoderT_(u). Let {circumflex over (t)}_(i) be the ith column of T_(u), fromLemma 1, Equation (22) can result

$\begin{matrix}{{P{\hat{t}}_{i}P^{2}} = {{{{{\hat{t}}_{i,g_{1}}{\hat{t}}_{g_{1},i}^{H}\mspace{14mu}\ldots} + {{\hat{t}}_{g_{N_{t,u},i}}{\hat{t}}_{g_{N_{t,u}},i}^{H}}} \approx {N_{t,u}/\left( {BN}_{t} \right)}} = \kappa}} & (22)\end{matrix}$and thus Equation (23) resultsH _(eff,u) :CN(0_(N) _(r) ,κI _(N) _(r) )  (23).

Similarly, the effective channel error matrix E_(eff u′)=

can distribute as shown in Equation (24)E _(eff,u′) :CN(0_(N) _(r) ,κε_(u) ² I _(N) _(r) )  (24)

The ergodic rate formula in Equation (20) can be interpreted as the rateof a MIMO channel under interference, then Equation (18) can beobtained, where η₁ and η₂ can be solutions to Equations (25) and (26):

$\begin{matrix}{{\eta_{1} + \frac{N_{r}\gamma_{u}\rho_{u}^{2}{\kappa\eta}_{1}}{{N_{r}\gamma_{u}\rho_{u}^{2}{\kappa\eta}_{1}} + 1} + {\sum\limits_{u^{\prime} \neq u}\frac{N_{r}\gamma_{u^{\prime}}\rho_{u}^{2}{\kappa ɛ}_{u}^{2}\eta_{1}}{{N_{r}\gamma_{u^{\prime}}\rho_{u}^{2}{\kappa ɛ}_{u}^{2}\eta_{1}} + 1}}} = 1} & (25) \\{{\eta_{2} + {\sum\limits_{u^{\prime} \neq u}\frac{N_{r}\gamma_{u^{\prime}}\rho_{u}^{2}{\kappa ɛ}_{u}^{2}\eta_{2}}{{N_{r}\gamma_{u^{\prime}}\rho_{u}^{2}{\kappa ɛ}_{u}^{2}\eta_{2}} + 1}}} = 1} & (26)\end{matrix}$

To verify the accuracy of the equivalent channel matrix, a cluster ofthree neighboring BSs can be considered, in which each cell of thecluster is divided into three sectors. The number of antenna can begiven as N_(t)=4 and N_(r)=2, and six mobile devices/users can berandomly placed in the area covered by the three sectors at clustercenter. In some embodiments, the mobile devices/users can be assumed tobe moving at the speed of 10 km/h, and the AR model of order 2 can beadopted. The cell edge SNR can be defined as the received SNR at thecell edge when one BS transmits at full power and other BSs are poweredoff.

FIG. 9 is an illustration of a graph of the sum rate versus cell edgeSNR with comparison of simulation and approximation for a selectednumber of antennas in accordance with various embodiments of thedisclosed subject matter. In the embodiment shown, N_(t)=4 and N_(r)=2.The asymptotic results compared with simulations can be as shown. Asshown, the largest difference between asymptotic and simulation resultsis around 20%. The results shown in FIG. 9 can also imply that for SU/MUmodes, some mode-switching can be employed for varying SNR and Dopplershift.

The scheduling component 212 can perform scheduling. In someembodiments, two-stage feedback can be received via the communicationcomponent 202 of the central control unit 200, and the schedulingcomponent 212 can schedule information to one or more mobiledevices/users as follows.

The two-stage feedback method can employ frame-level feedback that canbe used for mobile device/user scheduling. In some embodiments,frame-level feedback can be transmitted from the mobile devices/users tothe central control unit 200. For example, at the beginning of eachframe, each mobile device/user can send the average SNR from allcooperating BSs for the mobile device/user, and can also send themaximum Doppler shift. The average SNR and the maximum Doppler shift forthe mobile device/user can be sent to the central control unit 200, forexample. Based on such information, the asymptotic ergodic ratecalculation component 210 can evaluate the asymptotic ergodic rate foreach mobile device/user, and a set of mobile devices/users can beselected to receive inforamtion on the downlink during the currentframe.

To track the small-scale behaviors, the second stage of the two-stagefeedback can be transmitted from the mobile devices/users to the centralcontrol unit. The second stage of feedback can be slot-level feedback.The slot-level feedback can be applied to the selected mobiledevices/users in each frame. The small-scale channel coefficients at thelast symbol (which can be viewed as the pilot symbol) of each slot canbe sent to the central control unit. The channel coefficients at thepilot symbol of the next slot can be predicted using the AR modeldescribed in above-described AR model employed for channel prediction.The predicted channel coefficients for symbols in the next slot can beobtained with interpolation, and can be used to calculate the precoder.The update of channel coefficients typically occupies only limiteduplink bandwidth since the number of selected mobile devices/users istypically much smaller as compared to the total number of mobiledevices/users.

Consider a set of channel matrices {H_(u)}_(u=1) ^(U) for a network MIMOsystem. Let U={1, 2, . . . , U} denote the set of all mobiledevices/users, and U_(i) be a subset of U, where the cardinality ofU_(i) can be less than or equal to the maximum number of simultaneousmobile devices/users, which equals M=└BN_(t)/N_(r)┘ if the BD precodingis applied.

Table 1 illustrates pseudocode for one or more operations that can beperformed by the scheduling component 212 of the central control unit200 for downlink scheduling of selected mobile devices/users. In someembodiments, the pseudocode of Table 1 can be a scheduling algorithm foreach frame.

TABLE 1 Mobile device/User Scheduling Algorithm 1. For each mobiledevice/user u, calculate the asymptotic ergodic rate for SU mode and MUmode, denote as R_(su) ^(asym) (u) and R_(mu) ^(asym) (u), respectively.2. Find the best mobile device/user in SU mode, and the best set ofmobile devices/users in MU mode, according to weighted ergodic rate:${S_{su} = {\underset{u \in U}{\arg{\;\;}\max}{R_{su}^{asym}(u)}}},{S_{mu} = {\underset{U_{i}\underset{\_}{\Subset}U}{\arg{\;\;}\max}{\sum_{u \in U_{i}}{R_{mu}^{asym}(u)}}}}$3. Choose the service mode giving higher asymptotic ergodic rate, thatis, schedule the set of user(s) S by $S = \left\{ \begin{matrix}{S_{su},} & {{{if}\mspace{14mu}{\sum_{u \in S_{mu}}{\mu_{u}{R_{mu}(u)}}}} < {R_{su}\left( S_{su} \right)}} \\S_{{mu},} & {{otherwise}.}\end{matrix} \right.$

By varying the weighting factor μ_(u) (t), different schedulers can bedesigned. In various embodiments, the scheduling component 212 can be amaximum sum rate scheduler (MSRS) if μ_(u) (t)=1, ∀u, and the schedulingcomponent 212 can be a proportional fair scheduler (PFS) if μ_(u) (t)=1/R _(u)(t), ∀u. In various embodiments, R _(u) (t) can be the averagerate within a sliding window of time.

FIGS. 5, 6, 7, 8A and 8B are flowcharts of exemplary methods tofacilitate downlink scheduling in wireless communications systems inaccordance with various embodiments of the disclosed subject matter.

Turning first to FIG. 5, at 502, method 500 can include applying channelprediction at a transmitter for transmitting information to one or moremobile devices.

At 504, method 500 can include predicting channel state information fora channel over which the information is transmitted, the channel stateinformation being based, at least, on the channel prediction. In someembodiments, applying channel prediction at a transmitter can includeapplying channel prediction at a base station.

At 506, method 500 can include determining a precoding matrix to applyto the information, the determining the precoding matrix being based, atleast, on predicted channel state information.

At 508, method 500 can include scheduling transmission of theinformation to the one or more mobile devices based, at least, on anasymptotic ergodic rate for the one or more mobile devices. In someembodiments, the scheduling transmission of the information to the oneor more mobile devices based, at least, on an asymptotic ergodic ratefor the one or more mobile devices includes scheduling transmission ofthe information to the one or more mobile devices based, at least, onlarge-scale channel behavior. In some embodiments, the schedulingtransmission of the information to the one or more mobile devices based,at least, on an asymptotic ergodic rate for the one or more mobiledevices further includes scheduling transmission of the information tothe one or more mobile devices based, at least, on a maximum Dopplershift for the one or more mobile devices.

FIG. 6 is an illustration of a method of scheduling one or more mobiledevices. At 602, method 600 can include obtaining statisticalinformation of a channel over which the one or more mobile devicestransmit. At 604, method 600 can include determining an ergodic ratebased, at least, on the statistical information.

At 606, method 600 can include selecting one or more mobile devices forscheduling based, at least, on the ergodic rate.

At 608, method 600 can include scheduling the one or more mobile devicesbased, at least, on variation in the channel.

In some embodiments, although not shown, method 600 can also includeperforming channel prediction for the one or more mobile devicesselected for scheduling. The performing channel prediction can includeperforming channel prediction based, at least, on an auto-regressivemodel.

In some embodiments, although not shown, method 600 can includepredicting channel state information in one or more future slots forwhich the one or more mobile devices are scheduled.

FIG. 7 is an illustration of a method of scheduling downlinktransmission of information to one or more mobile devices based on atwo-stage feedback method.

At 702, method 700 can include receiving, at a first location in aframe, frame-level feedback from the one or more mobile devices. In someembodiments, receiving the frame-level feedback can include: receivingsignal-to-noise ratio (SNR) information from the one or more mobiledevices, the SNR being from one or more cooperating base stations; andreceiving Doppler shift information from the one or more mobile devices.In some embodiments, receiving the SNR can include receiving an averageSNR. In some embodiments, receiving the Doppler shift information caninclude receiving a maximum Doppler shift.

At 704, method 700 can include determining an asymptotic ergodic ratebased, at least, on the frame-level feedback. At 706, method 700 caninclude selecting at least one of the one or more mobile devices toreceive the downlink transmission of information during the frame.

In some embodiments, although not shown, method 700 can includereceiving slot-level feedback from the at least one of the one or moremobile devices selected for transmission during the frame. Theslot-level feedback can include channel coefficients at a symbol of aslot of the frame. In some embodiments, the symbol of the slot is atleast one of a last symbol of the slot of the frame or a pilot symbol.

In some embodiments, method 700 can also include applying the slot-levelfeedback.

In various embodiments, method 700 can include predicting channelcoefficients at the symbol of a next slot, the predicting being based ona model of a channel for which channel coefficients are predicted. Insome embodiments, the predicting being is based on an auto-regressivemodel of the channel. In some embodiments, predicting channelcoefficients in the next slot is based on interpolation.

In various embodiments, method 700 can also include calculating aprecoder based on the channel coefficients predicted for the next slot.

Turning now to FIGS. 8A and 8B, method 800 can be as follows. At 802,method 800 can include calculating, for a frame in which one or moremobile devices are scheduled, an asymptotic ergodic rate for single usermode and multi-user mode for the one or more mobile devices.

At 804, method 800 can include calculating, for the frame, a weightedergodic rate based, at least, on the asymptotic ergodic rate. In someembodiments, calculating the weighted ergodic rate can include weightingthe asymptotic ergodic rate by a weighting factor associated withmaximum sum rate scheduling. In some embodiments, calculating theweighted ergodic rate comprises weighting the asymptotic ergodic rate bya weighting factor associated with proportional fair scheduling.

At 806, method 800 can include selecting a mobile device in the singleuser mode, and selecting a set of mobile devices in the multi-user mode,the selecting the mobile device and the selecting the set of mobiledevices being based, at least, on the weighted ergodic rate.

At 808, method 800 can include determining a first weighted asymptoticergodic rate associated with the single user mode. At 810, method 800can include determining a second weighted asymptotic ergodic rateassociated with the multi-user mode.

At 812, method 800 can include selecting at least one of the single usermode or the multi-user mode, the selecting comprising selecting a modeassociated with a higher one of the first weighted asymptotic ergodicrate and the second weighted asymptotic ergodic rate.

At 814, method 800 can include scheduling the one or more mobile devicesto receive information in a selected one of the single user mode or themulti-user mode.

For simplicity of explanation, the methods are depicted and described asa series of acts. It is to be understood and appreciated that thevarious embodiments of the subject disclosure is not limited by the actsillustrated and/or by the order of acts, for example acts can occur invarious orders and/or concurrently, and with other acts not presentedand described herein. Furthermore, not all illustrated acts may berequired to implement the methods in accordance with the disclosedsubject matter. In addition, those skilled in the art will understandand appreciate that the methods could alternatively be represented as aseries of interrelated states by way of state diagram or events.Additionally, it should be further appreciated that the methodsdisclosed hereinafter and throughout this specification are capable ofbeing stored on an article of manufacture to facilitate transporting andtransferring such methods to computers. The term article of manufacture,as used herein, can encompass a computer program accessible from anycomputer-readable device, carrier, or media.

FIGS. 9, 10 and 11 illustrate exemplary simulation and numerical resultsin accordance with embodiments of the disclosed subject matter. Turningfirst to FIG. 9, FIG. 9 is an exemplary graph of sum rate versus celledge signal-to-noise ratio (SNR) with comparison of simulation andapproximation for a selected number of antennas in accordance withvarious embodiments of the disclosed subject matter.

The performance of different scheduling methods for a cluster with thesame setting as FIG. 9 can be described below. The simulation process isdivided into 10000 frames, and it is assumed that within one frame, thelarge-scale fading behavior and the velocity of mobile devices/users areapproximately constant. The frame structure can be defined such that, inone frame, there are 10 slots. In some embodiments, each of the 10 slotsincludes 10 symbols, with symbol duration of approximately 10⁻⁴ s. Themobile devices/users can be assumed to randomly move at speeds betweenapproximately 0-40 km/h. An AR model order of 2 can be assumed forslot-level CSIT prediction.

In various embodiments, the following scheduling methods can beconsidered for performance comparison. In some embodiments,Opportunistic Scheduling with Instantaneous CSI (OSICSI) can becompared. In some embodiments, the CSIT can be perfectly known to allthe BSs in the cluster, and the mobile devices/users scheduled for eachsymbol can be selected in a greedy manner to maximize the weighted sumrate. Opportunistic Scheduling with Predicted CSI (OSPCSI) can also becompared. The OSPCSI can include a greedy sum-rate maximizingopportunistic scheduler, while the mobile device/user selection is basedon the predicted CSIT.

FIG. 10 is an exemplary graph of sum capacity versus number of mobiledevices/users employing downlink scheduling in accordance with variousembodiments of the disclosed subject matter. In some embodiments, thesum rate can be as follows. The graph illustrates the sum rate fordifferent the scheduling methods described herein compared with theOSICSI and OSPCSI methods. For all methods, the sum rates increase withthe number of mobile devices/users and saturate gradually as a result ofthe multi-user diversity effect. With imperfect per-symbol CSIT, Theperformance of OSPCSI method lies between the OSICSI method and theMSRS. Even with “coarse” mobile device/user selection and imperfectCSIT, the MSRS performs well while the feedback amount is largelyreduced. For example, at edge SNR of 15 dB and totally 15 mobiledevices/users, the MSRS achieves 73% and 90% of the sum rate of OSICSIand OSPCSI methods, respectively. The effect of multiuser diversity isnot very apparent for PFS, since it does not always choose mobiledevices/users under best channel condition.

FIG. 11 is an exemplary graph of an Average Jain's Fairness Index versusobservation window size employing downlink scheduling in accordance withvarious embodiments of the disclosed subject matter. Fairness can be asconsidered below. The graph shows the average Jain's fairness indexversus observation window size. In varoius embodiments, the Jain'sfairness index can be adopted for fairness comparison. The Jain'sfairness index versus varying window size in slots is depicted in FIG.12 in which the edge SNR is 15 dB and there are 30 mobile devices/usersin total. While the Jain's fairness index is employed for the simulationresults shown in FIG. 12, in other embodiments, any number of otherdifferent types of fairness indices and/or methods of fairnesscomparison thereof can be employed.

As expected, there is a large penalty in fairness with the two sum-ratemaximizing algorithms (MSRS and OSPCSI). For the PFS, the averagefairness is poor for small window size, but the long-term fairness isquite good.

FIG. 12 illustrates an exemplary environment 1200 for implementingvarious embodiments as described herein. The exemplary environment caninclude a computer 1202. The computer 1202 can include a processing unit1204, a system memory 1206 and a system bus 1208. The system bus 1208can couple various system components including, but not limited to,coupling the system memory 1206 to the processing unit 1204. Theprocessing unit 1204 can be any of various processors. In someembodiments, dual microprocessors and other multi-processorarchitectures may also be employed as the processing unit 1204.

The system bus 1208 can be any of several types of bus structure thatcan interconnect to a memory bus (with or without a memory controller),a peripheral bus, and a local bus using any bus architecture. The systemmemory 1206 can include read-only memory (ROM) 1210 and random accessmemory (RAM) 1212. A basic input/output system (BIOS) is stored in anon-volatile memory such as ROM, erasable programmable read only memory(EPROM), electrically erasable programmable read only memory (EEPROM).The BIOS can contain the basic routines that help to transferinformation between elements within the computer 1202, such as duringstart-up. The RAM 1212 can also include a high-speed RAM such as staticRAM for caching data.

The computer 1202 can also include an internal hard disk drive (HDD)1214 (e.g., EIDE, SATA). The internal hard disk drive 1214 can also beconfigured for external use in a suitable chassis (not shown). Thecomputer 1202 can also include a magnetic floppy disk drive (FDD) 1216,(e.g., to read from or write to a removable diskette 1218) and anoptical disk drive 1220, (e.g., reading a CD-ROM disk 1222 or, to readfrom or write to other high capacity optical media such as the DVD). Thehard disk drive 1214, magnetic disk drive 1216 and/or optical disk drive1220 can be connected to the system bus 1208 by a hard disk driveinterface 1224, a magnetic disk drive interface 1226 and/or an opticaldrive interface 1228. The interface 1224 for external driveimplementations can include, but is not limited to, Universal Serial Bus(USB) and IEEE1394 interface technologies. Other external driveconnection technologies are within contemplation of the subject matterdisclosed herein.

The drives and their associated computer-readable media can providenonvolatile storage of data, data structures and/or computer-executableinstructions. For the computer 1202, the drives and media canaccommodate the storage of any data in a suitable digital format.Although the description of computer-readable media above refers to aHDD, a removable magnetic diskette, and/or a removable optical mediasuch as a CD or DVD, it should be appreciated by those skilled in theart that other types of media, which are readable by a computer (e.g.,zip drives, magnetic cassettes, flash memory cards, cartridges) can alsobe used in the exemplary operating environment, and further, that anysuch media can contain computer-executable instructions for performingthe methods and/or implementing the systems of the various embodiments.

A number of program modules can be stored in the drives and RAM 1212,including an operating system 1230, one or more application programs1232, other program modules 1234 and/or program data 1236. All orportions of the operating system, applications, modules, and/or data canalso be cached in the RAM 1212. It is appreciated that the variousembodiments can be implemented with various different operating systemsor combinations thereof.

A user can enter commands and information into the computer 1202 throughone or more wired/wireless input devices (e.g., a keyboard 1238 and apointing device, such as a mouse 1240). Other input devices (not shown)may include a microphone, an IR remote control, a joystick, a game pad,a stylus pen, touch screen or the like. These and other input devicescan be connected to the processing unit 1204 through an input deviceinterface 1242 that is coupled to the system bus 1208 in someembodiments. In other embodiments, the input devices can be connected tothe processing unit 1204 via other interfaces (e.g., parallel port, anIEEE1394 serial port, a game port, a USB port, an IR interface).

A monitor 1244 or other type of display device can be connected to thesystem bus 1208 via an interface, such as a video adapter 1246. Inaddition to the monitor 1244, other peripheral output devices (notshown) (e.g., speakers, printers) can be connected to the system bus1208.

The computer 1202 can operate in a networked environment using logicalconnections via wired and/or wireless communications to one or moreremote computers, such as a remote computer 1248. The remote computer1248 can be a workstation, a server computer, a router, a personalcomputer, portable computer, microprocessor-based entertainmentappliance, a peer device and/or other common network node. The remotecomputer 1248 can include one or more of the elements described for thecomputer 1202, although, for purposes of brevity, only a memory/storagedevice 1250 is illustrated. The logical connections depicted can includewired/wireless connectivity to a local area network (LAN) 1252 and/orlarger networks, such as wide area network (WAN) 1254. Such LAN and WANnetworking environments are commonplace in offices and companies, andcan facilitate enterprise-wide computer networks, such as intranets. TheLAN, WAN and other networking environments can connect to a globalcommunications network (e.g., the Internet).

When used in a LAN networking environment, the computer 1202 can beconnected to the local network 1252 through a wired and/or wirelesscommunication network interface or adapter 1256. The adapter 1256 canfacilitate wired or wireless communication to the LAN 1252, which canalso include a wireless access point disposed thereon for communicatingwith the wireless adapter 1256.

When used in a WAN networking environment, the computer 1202 can includea modem 1258, can be connected to a communications server on the WAN1254 and/or can have other functionality and/or structure forestablishing communications over the WAN 1254. The modem 1258, which canbe internal or external, and which can be a wired or wireless device,can be connected to the system bus 1208 via the serial port interface1242. In a networked environment, program modules depicted relative tothe computer 1202, or portions thereof, can be stored in the remotememory/storage device 1250. It will be appreciated that the networkconnections shown are exemplary and other functionality and/or structurefor establishing a communications link between the computers can beused.

The computer 1202 can be operable to communicate with any wirelessdevices or entities operatively disposed in wireless communication(e.g., a printer, scanner, desktop and/or portable computer, portabledata assistant, communications satellite, any piece of equipment orlocation associated with a wirelessly detectable tag (e.g., a kiosk,news stand, restroom) and telephone). Such can include, but is notlimited to, Wi-Fi (Wireless Fidelity) and/or BLUETOOTH™ wirelesstechnologies. Thus, the communication can be a predefined structure aswith a conventional network or simply an ad hoc communication between atleast two devices.

Wi-Fi can allow connection to the Internet from a couch at home, a bedin a hotel room, or a conference room at work, without wires. Wi-Fi is awireless technology similar to that used in a cell phone that enablessuch devices to send and receive data indoors and out and/or anywherewithin the range of a BS. Wi-Fi networks can use radio technologiescalled IEEE802.11 (a, b, g, n, etc.) to provide secure, reliable, fastwireless connectivity. A Wi-Fi network can be used to connect computersto each other, to the Internet, and/or to wired networks (which can useIEEE802.3 or Ethernet). Wi-Fi networks can operate in the unlicensed 2.4and 5 GHz radio bands, at an 11 Mbps (802.11a) or 54 Mbps (802.11b) datarate, for example, or with products that contain both bands (dual band).As such, networks employing Wi-Fi technology can provide real-worldperformance similar to the basic 10BaseT wired Ethernet networks used inmany offices.

It is to be appreciated and understood that components as described withregard to a particular system or method, can include the same or similarfunctionality as respective components as described with regard to othersystems or methods disclosed herein.

As it employed in the specification, the term “processor” can refer tosubstantially any computing processing unit or device comprising, butnot limited to comprising, single-core processors; single-processorswith software multithread execution capability; multi-core processors;multi-core processors with software multithread execution capability;multi-core processors with hardware multithread technology; parallelplatforms; and parallel platforms with distributed shared memory.

Additionally, a processor can refer to an integrated circuit, anapplication specific integrated circuit (ASIC), a digital signalprocessor (DSP), a field programmable gate array (FPGA), a programmablelogic controller (PLC), a complex programmable logic device (CPLD), adiscrete gate or transistor logic, discrete hardware components, or anycombination thereof designed to perform the functions described herein.Processors can exploit nano-scale architectures such as, but not limitedto, molecular and quantum-dot based transistors, switches and gates, inorder to optimize space usage or enhance performance of user equipment.A processor can also be implemented as a combination of computingprocessing units.

In the specification, terms such as “data store,” data storage,”“database,” and substantially any other information storage componentrelevant to operation and functionality of a component, refer to “memorycomponents,” or entities embodied in a “memory” or components comprisingthe memory. For example, information relevant to operation of variouscomponents described in the disclosed subject matter, and that can bestored in a memory, can comprise, but is not limited to comprising,subscriber information; cell configuration or service policies andspecifications; privacy policies; and so forth. It will be appreciatedthat the memory components described herein can be either volatilememory or nonvolatile memory, or can include both volatile andnonvolatile memory. By way of illustration, and not limitation,nonvolatile memory can include read only memory (ROM), programmable ROM(PROM), electrically programmable ROM (EPROM), electrically erasable ROM(EEPROM), phase change memory (PCM), flash memory, or nonvolatile RAM(e.g., ferroelectric RAM (FeRAM)). Volatile memory can include randomaccess memory (RAM), which acts as external cache memory. By way ofillustration and not limitation, RAM is available in many forms such assynchronous RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM),double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), SynchlinkDRAM (SLDRAM), and direct Rambus RAM (DRRAM). Additionally, thedisclosed memory components of systems or methods herein are intended tocomprise, without being limited to comprising, these and any othersuitable types of memory.

Various embodiments or features described herein can be implemented as amethod, apparatus, or article of manufacture using standard programmingand/or engineering techniques. The term “article of manufacture” as usedherein is intended to encompass a computer program accessible from anycomputer-readable device, carrier, or media. For example, computerreadable media can include but are not limited to magnetic storagedevices (e.g., hard disk, floppy disk, magnetic strips), optical disks(e.g., compact disk (CD), digital versatile disk (DVD), Blu-ray disc),smart cards, and flash memory devices (e.g., card, stick, key drive).

What has been described above includes exemplary various embodiments. Itis, of course, not possible to describe every conceivable combination ofcomponents or methods for purposes of describing the embodiments, butone of ordinary skill in the art can recognize that many furthercombinations and permutations are possible. Accordingly, the detaileddescription is intended to embrace all such alterations, modifications,and variations that fall within the spirit and scope of the appendedclaims.

In particular and in regard to the various functions performed by theabove described components, devices, circuits, systems and the like, theterms (including any references to a “means”) used to describe suchcomponents are intended to correspond, unless otherwise indicated, toany component which performs the specified function of the describedcomponent (e.g., a functional equivalent), even though not structurallyequivalent to the disclosed structure, which performs the function inthe herein illustrated exemplary embodiments of the embodiments. In thisregard, it will also be recognized that the embodiments includes asystem as well as a computer-readable medium having computer-executableinstructions for performing the acts and/or events of the variousmethods.

In addition, while a particular feature can have been disclosed withrespect to only one of several implementations, such feature can becombined with one or more other features of the other implementations ascan be desired and advantageous for any given or particular application.Furthermore, to the extent that the terms “includes,” and “including”and variants thereof are used in either the detailed description or theclaims, these terms are intended to be inclusive in a manner similar tothe term “comprising”, such as, for example, as the term “comprising” isinterpreted when employed as a transitional word in a claim.

Referring to FIG. 13, illustrated is a block diagram of an exemplary,non-limiting electronic device 1300 that can perform downlink schedulingfor wireless network components in accordance with an aspect of thedisclosed subject matter. The electronic device 1300 can include, but isnot limited to, a central control unit (e.g., central control unit 200),a BS, a mobile device, a computer, a laptop computer, or networkequipment (e.g., routers, access points, femtocells, picocells) and thelike.

Components of the electronic device 1300 can include, but are notlimited to, a processor component 1302, a system memory 1304 (withnonvolatile memory 1306), and a system bus 1308 that can couple varioussystem components including the system memory 1304 to the processorcomponent 1302. The system bus 1308 can be any of various types of busstructures including a memory bus or memory controller, a peripheralbus, or a local bus using any of a variety of bus architectures.

Computing devices typically include a variety of media, which caninclude computer-readable storage media or communications media, whichtwo terms are used herein differently from one another as follows.

Computer-readable storage media can be any available storage media thatcan be accessed by the computer and includes both volatile andnonvolatile media, removable and non-removable media. By way of example,and not limitation, computer-readable storage media can be implementedin connection with any method or technology for storage of informationsuch as computer-readable instructions, program modules, structureddata, or unstructured data. Computer-readable storage media can include,but are not limited to, RAM, ROM, EEPROM, flash memory or other memorytechnology, CD-ROM, digital versatile disk (DVD) or other optical diskstorage, magnetic cassettes, magnetic tape, magnetic disk storage orother magnetic storage devices, or other tangible and/or non-transitorymedia which can be used to store desired information. Computer-readablestorage media can be accessed by one or more local or remote computingdevices, e.g., via access requests, queries or other data retrievalprotocols, for a variety of operations with respect to the informationstored by the medium.

Communications media typically embody computer-readable instructions,data structures, program modules or other structured or unstructureddata in a data signal such as a modulated data signal (e.g., a carrierwave or other transport mechanism) Sand includes any informationdelivery or transport media. The terms “modulated data signal” or“signals” refer to a signal that has one or more of its characteristicsset or changed in such a manner as to encode information in one or moresignals. By way of example, and not limitation, communication mediainclude wired media, such as a wired network or direct-wired connection,and wireless media such as acoustic, RF, infrared and other wirelessmedia.

The system memory 1304 can include computer-readable storage media inthe form of volatile and/or nonvolatile memory 1306. A basicinput/output system (BIOS), containing the basic routines that help totransfer information between elements within electronic device 1300,such as during start-up, can be stored in memory 1304. Memory 1304 cantypically contain data and/or program modules that can be immediatelyaccessible to and/or can be operated on by processor component 1302. Byway of example, and not limitation, system memory 1304 can also includean operating system, application programs, other program modules, andprogram data. As a further example, system memory can include programmodules for downlink scheduling.

The nonvolatile memory 1306 can be removable or non-removable. Forexample, the nonvolatile memory 1306 can be in the form of a removablememory card or a USB flash drive. In accordance with one aspect, thenonvolatile memory 1306 can include flash memory (e.g., single-bit flashmemory, multi-bit flash memory), ROM, PROM, EPROM, EEPROM, and/or NVRAM(e.g., FeRAM), or a combination thereof, for example. Further, the flashmemory can include NOR flash memory and/or NAND flash memory.

A user can enter commands and information into the electronic device1300 through input devices (not illustrated) such as a keypad,microphone, tablet or touch screen although other input devices can alsobe utilized. These and other input devices can be connected to theprocessor component 1302 through input interface component 1310 that canbe connected to the system bus 1308. Other interface and bus structures,such as a parallel port, game port or a universal serial bus (USB) canalso be utilized. A graphics subsystem (not illustrated) can also beconnected to the system bus 1308. A display device (not illustrated) canbe also connected to the system bus 1308 via an interface, such asoutput interface component 1312, which can in turn communicate withvideo memory. In addition to a display, the electronic device 1300 canalso include other peripheral output devices such as speakers (notillustrated), which can be connected through output interface component1312. In an aspect, other electronic devices, e.g., other BSs and/ormobile devices in a network can be communicatively coupled to electronicdevice 1500 by way of input interface component 1310 and outputinterface component 1312, which can facilitate transfer of feedbackand/or downlink scheduling information.

It is to be understood and appreciated that the computer-implementedprograms and software can be implemented within a standard computerarchitecture. While some aspects of the disclosure have been describedabove in the general context of computer-executable instructions thatcan run on one or more computers, those skilled in the art willrecognize that the technology also can be implemented in combinationwith other program modules and/or as a combination of hardware andsoftware.

Generally, program modules include routines, programs, components and/ordata structures that perform particular tasks or implement particularabstract data types. Moreover, those skilled in the art will appreciatethat the inventive methods can be practiced with other computer systemconfigurations, including single-processor or multiprocessor computersystems, minicomputers, mainframe computers, as well as personalcomputers, hand-held computing devices (e.g., PDA, phone),microprocessor-based or programmable consumer electronics, and the like,each of which can be operatively coupled to one or more associateddevices.

As utilized herein, terms “component,” “system,” “interface,” and thelike, can refer to a computer-related entity, either hardware, software(e.g., in execution), and/or firmware. For example, a component can be aprocess running on a processor, a processor, an object, an executable, aprogram, and/or a computer. By way of illustration, both an applicationrunning on a server and the server can be a component. One or morecomponents can reside within a process and a component can be localizedon one computer and/or distributed between two or more computers.

Furthermore, the disclosed subject matter can be implemented as amethod, apparatus, or article of manufacture using standard programmingand/or engineering techniques to produce software, firmware, hardware,or any combination thereof to control a computer to implement thedisclosed subject matter. The term “article of manufacture” as usedherein is intended to encompass a computer program accessible from anycomputer-readable device, carrier, or media. For example, computerreadable media can include but are not limited to magnetic storagedevices (e.g., hard disk, floppy disk, magnetic strips), optical disks(e.g., compact disk (CD), digital versatile disk (DVD)), smart cards,and flash memory devices (e.g., card, stick, key drive). Additionally itshould be appreciated that a carrier wave can be employed to carrycomputer-readable electronic data such as those used in transmitting andreceiving electronic mail or in accessing a network such as the Internetor a local area network (LAN). Of course, those skilled in the art willrecognize many modifications can be made to this configuration withoutdeparting from the scope or spirit of the disclosed subject matter.

Some portions of the detailed description can have been presented interms of algorithms and/or symbolic representations of operations ondata bits within a computer memory. These algorithmic descriptionsand/or representations are the means employed by those cognizant in theart to most effectively convey the substance of their work to othersequally skilled. An algorithm is here, generally, conceived to be aself-consistent sequence of acts leading to a desired result. The actsare those requiring physical manipulations of physical quantities.Typically, though not necessarily, these quantities take the form ofelectrical and/or magnetic signals capable of being stored, transferred,combined, compared, and/or otherwise manipulated.

It has proven convenient at times, principally for reasons of commonusage, to refer to these signals as bits, values, elements, symbols,characters, terms, numbers, or the like. It should be borne in mind,however, that all of these and similar terms are to be associated withthe appropriate physical quantities and are merely convenient labelsapplied to these quantities. Unless specifically stated otherwise asapparent from the foregoing discussion, it is appreciated thatthroughout the disclosed subject matter, discussions utilizing termssuch as processing, computing, calculating, determining, and/ordisplaying, and the like, refer to the action and processes of computersystems, and/or similar consumer and/or industrial electronic devicesand/or machines, that manipulate and/or transform data represented asphysical (electrical and/or electronic) quantities within the computer'sand/or machine's registers and memories into other data similarlyrepresented as physical quantities within the machine and/or computersystem memories or registers or other such information storage,transmission and/or display devices.

What has been described above includes examples of aspects of thedisclosed subject matter. It is, of course, not possible to describeevery conceivable combination of components or methodologies forpurposes of describing the disclosed subject matter, but one of ordinaryskill in the art can recognize that many further combinations andpermutations of the disclosed subject matter are possible. Accordingly,the disclosed subject matter is intended to embrace all suchalterations, modifications and variations that fall within the spiritand scope of the appended claims. Furthermore, to the extent that theterms “includes,” “has,” or “having,” or variations thereof, are used ineither the detailed description or the claims, such terms are intendedto be inclusive in a manner similar to the term “comprising” as“comprising” is interpreted when employed as a transitional word in aclaim.

What is claimed is:
 1. A method, comprising: applying, by a devicecomprising a processor, channel prediction at a base station device fortransmitting information to one or more mobile devices of a plurality ofmobile devices, wherein the device is distinct from the one or moremobile devices; predicting channel state information for a downlinkchannel over which the information is transmitted, the channel stateinformation being based, at least, on the channel prediction;determining a precoding matrix to apply to the information transmittedover the downlink channel from the base station device based, at least,on the channel state information; and scheduling transmission of theinformation to the one or more mobile devices of the plurality of mobiledevices, wherein the scheduling comprises: receiving, from the pluralityof mobile devices, respective frame-level feedback at a first portion ofa defined frame, wherein the respective frame-level feedback comprisesrespective average signal-to-noise ratios from cooperating base stationdevices for the set of mobile devices and respective Doppler shiftinformation for the plurality of mobile devices; and scheduling thetransmission to the one or more mobile devices of the plurality ofmobile devices on the downlink channel during the defined frame, whereinthe one or more mobile devices to which the transmission is made isselected based on an evaluation of respective asymptotic ergodic ratesfor the plurality of mobile devices.
 2. The method of claim 1, whereinthe respective asymptotic ergodic rates are based on the respectiveaverage signal-to-noise ratios and the respective Doppler shiftinformation for the plurality of mobile devices.
 3. The method of claim1, wherein the respective Doppler shift information comprises respectivemaximum Doppler shifts for the plurality of mobile devices.
 4. A devicehaving a processor, comprising: a channel prediction componentconfigured to apply channel prediction at a base station device fortransmission of information from the base station device to one or moremobile devices; a channel state information prediction componentconfigured to predict channel state information for a channel over whichthe information is transmitted, the channel state information beingbased, at least, on the channel prediction applied by the channelprediction component; a precoding matrix component configured todetermine a precoding matrix to apply to the information based, atleast, on the channel state information from the channel stateinformation component; and a scheduling component configured to schedulethe transmission of the information from the base station device to theone or more mobile devices based, at least, on an asymptotic ergodicrate for the one or more mobile devices, wherein the schedulingcomprises a first stage and a second stage of feedback from the one ormore mobile devices, wherein the first stage of feedback comprisesframe-level feedback associated with signal-to-noise information andDoppler shift information received from the one or more mobile devices,and wherein the second stage of feedback comprises slot-level feedbackassociated with a small-scale channel coefficient for a slot receivedfrom the one or more mobile devices.
 5. The device of claim 4, whereinthe device is a central control unit distinct from the base stationdevice.
 6. The device of claim 4, wherein the asymptotic ergodic ratefor the one or more mobile devices is based, at least, on large-scalechannel behavior.
 7. The device of claim 4, wherein the asymptoticergodic rate for the one or more mobile devices is based, at least, on amaximum Doppler shift for the one or more mobile devices.
 8. Anon-transitory computer-readable storage medium havingcomputer-executable instructions that, in response to execution, cause adevice including a processor to perform operations, comprising:determining information indicative of channel prediction at a basestation device, wherein the information is associated with channel stateinformation for a channel from the base station device to a receiverdevice; and scheduling transmission of data to a plurality of mobiledevices, wherein the scheduling comprises, for the plurality of mobiledevices: computing respective first asymptotic ergodic rates for a firstmode and computing respective second asymptotic ergodic rates for asecond mode; and scheduling the transmission according to the first modebased on a determination that a first asymptotic ergodic rate of therespective first asymptotic ergodic rates is larger than a secondasymptotic ergodic rate of the respective second asymptotic ergodicrates, and scheduling the transmission according to the second modebased on a determination that the second asymptotic ergodic rate islarger than the first asymptotic ergodic rate.
 9. The non-transitorycomputer-readable storage medium of claim 8, wherein the scheduling thetransmission of the data comprises scheduling the transmission of thedata to a mobile device during a defined time frame.